Electric vehicles typically have an electric motor/generator that provides electric power to an output member that is mechanically connected to vehicle wheels through a drive train to propel the vehicle. Some electric vehicles include an auxiliary power unit (APU) that generates electric power to supplement power provided by a battery. The APU may include an engine, such as an internal combustion engine, that powers a generator that generates electric power. In order to limit emissions and increase fuel economy, the APU is typically used only as needed, with the battery serving as the primary source of electric power. One known control method is thermostatic control (also referred to as “bang-bang” control), in which the APU is turned on and off depending upon the battery charge level, and provides a fixed power level that provides a high energy conversion efficiency. During lightly-loaded driving cycles, this control strategy may result in relatively frequent engine on-off events, and potentially, a corresponding increase in emissions. Another control method is referred to as a “load-following” method, as the power provided by the APU follows the total power demand from the vehicle operator and auxiliary loads. Because the APU is not necessarily operating within a desired efficiency range under this method, this method is typically used only when the buffer of available battery energy is relatively small, and would not be a preferred method for a battery electric vehicle with large energy storage capability.